{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/m2/n_wl3_4d45bdp1pp62mx45140000gn/T/ipykernel_91529/3019147123.py:22: RuntimeWarning: overflow encountered in exp\n",
      "  return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(np.log(i0e(r))+r)\n",
      "/var/folders/m2/n_wl3_4d45bdp1pp62mx45140000gn/T/ipykernel_91529/3019147123.py:22: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(np.log(i0e(r))+r)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.special import i0,i1,iv\n",
    "from scipy.special import i0e,i1e,ive\n",
    "from scipy import integrate\n",
    "from scipy import optimize\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def qCorrs(betaJ,q):\n",
    "    def integrandabcd(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(i1e(r)/i0e(r))**4\n",
    "    def integrandabc(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(ive(2,r)*i1e(r)**2/i0e(r)**3+i1e(r)**2/i0e(r)**2)/2\n",
    "    def integrandab(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(1+ive(2,r)**2/i0e(r)**2)/2\n",
    "    upLim=200\n",
    "    corrabcd=integrate.quad(integrandabcd,0,upLim)[0]-q**2 #(n choose 4)*3*2\n",
    "    corrabc=integrate.quad(integrandabc,0,upLim)[0]-q**2 #n*(n-1)*(n-2)\n",
    "    corrab=integrate.quad(integrandab,0,upLim)[0]-q**2 #n choose 2\n",
    "    return corrabcd,corrabc,corrab\n",
    "def Ztheta(betaJ,q):\n",
    "    def integrandZ(r):\n",
    "        return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(np.log(i0e(r))+r)\n",
    "    upLim=200\n",
    "    Z=integrate.quad(integrandZ,0,upLim)[0]+betaJ**2*(1-q)\n",
    "    return Z\n",
    "def logZ(betaJ,q):\n",
    "    logZ=-betaJ**2/2+betaJ**2*q**2/2+Ztheta(betaJ,q)\n",
    "    return logZ\n",
    "betaJs=np.arange(0.01,2.0,0.01)\n",
    "qs=np.zeros(len(betaJs))\n",
    "replicons=np.zeros(len(betaJs))\n",
    "for betaJ in betaJs:\n",
    "    res=optimize.minimize_scalar(lambda q: logZ(betaJ,q),bounds=(0,1),method='bounded')\n",
    "    q=res.x\n",
    "    qs[betaJ==betaJs]=q\n",
    "    #print(np.round(betaJ,1),q,getQ(betaJ))\n",
    "    secqDeriv=(Ztheta(betaJ,q+0.01)-2*Ztheta(betaJ,q)+Ztheta(betaJ,q-0.01))/0.01**2\n",
    "    #print(q)\n",
    "    corrabcd,corrabc,corrab=qCorrs(betaJ,q)\n",
    "    #2*(-1/2*corrab+2*corrabc-3/2*corrabcd)*2*betaJ**2\n",
    "    #print(secqDeriv,4*(-1/2*corrab+2*corrabc-3/2*corrabcd)*betaJ**4)\n",
    "    r=4*(corrab-2*corrabc+corrabcd)*(2*betaJ**2)**2-8*betaJ**2\n",
    "    replicons[betaJ==betaJs]=r\n",
    "plt.plot(betaJs,replicons)\n",
    "plt.xlabel(r'$\\beta J$')\n",
    "plt.ylabel(\"Replicon Mass\")\n",
    "plt.hlines(0,0,2,color='black',linestyles='dashed')\n",
    "plt.title(\"Replicon Mass\")\n",
    "plt.savefig(\"repliconMass.pdf\",bbox_inches='tight',dpi='figure')\n",
    "plt.show()\n",
    "plt.plot(betaJs,qs)\n",
    "plt.xlabel(r'$\\beta J$')\n",
    "plt.ylabel(r'$q$')\n",
    "plt.title(r\"Replica Order Appears at $\\beta J=1.0$\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5200617415214036"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.special import jv\n",
    "from scipy.integrate import quad\n",
    "def integrandm0(betaJ,r, q):\n",
    "    return (r / (2*q * betaJ**2)) * np.exp(-1 / (4*q * betaJ**2) * r**2)*(np.log(i0e(r))+r)\n",
    "def logZm0(betaJ,q):\n",
    "    first_term = -(betaJ**2 / 2)\n",
    "    second_term = (betaJ**2 / 2) * q**2\n",
    "\n",
    "    integrand_func = lambda r: integrandm0(betaJ,r, q)\n",
    "    integral = quad(integrand_func, 0, 50)[0]\n",
    "\n",
    "    third_term = (betaJ**2 ) * (1 - q)\n",
    "    fourth_term = integral\n",
    "\n",
    "    result = first_term + second_term + third_term + fourth_term\n",
    "    return result.real\n",
    "def getQ(betaJ):\n",
    "    res=optimize.minimize_scalar(lambda q: logZm0(betaJ,q),bounds=(0,1),method='bounded')\n",
    "    q=res.x\n",
    "    return q\n",
    "getQ(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9802982525143844"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def integrandabcd(r):\n",
    "    return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(i1e(r)/i0e(r))**4\n",
    "def integrandabc(r):\n",
    "    return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(ive(r,2)*i1e(r)**2/i0e(r)**3+i1e(r)**2/i0e(r)**2)/2\n",
    "def integrandab(r):\n",
    "    return r/(2*q*betaJ**2)*np.exp(-r**2/(4*q*betaJ**2))*(1+ive(r,2)**2/i0e(r)**2)/2\n",
    "r=100\n",
    "(1+ive(2,r)**2/i0e(r)**2)/2"
   ]
  }
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